Physics · Physical world and measurement · chapter 1 of 14

Class 11 Physics Chapter 1: Units and Measurement case study question with answers

One case-based question of the kind CBSE-pattern school exams ask: a passage and a table, then 3 parts worth 4 marks in all, with the answer and the marking scheme for each. Written from the NCERT chapter.

Case study · 4 marks

Meera finds the density of a rectangular glass slab in the school laboratory. She measures the length and the breadth with vernier callipers and the thickness with a metre scale, and the mass on a balance. Her readings are in the table. She enters them in a calculator, which shows the volume as 9.68876 cm³ and the density as 2.59059 g cm⁻³. Her teacher asks her to report every result to the correct number of significant figures.

quantity	length	breadth	thickness	mass
reading	5.24 cm	2.15 cm	0.86 cm	25.1 g

Part 1 · 1 mark

The number of significant figures in the thickness reading, 0.86 cm, is

(a) 3(b) 2(c) 1(d) 4

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Answer: (b) 2

The zero before the decimal point is never significant; 8 and 6 are: two figures.

Part 2 · 1 mark

Which reading limits the number of significant figures in the volume of the slab?

(a) the length, 5.24 cm(b) the breadth, 2.15 cm(c) the mass, 25.1 g(d) the thickness, 0.86 cm

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Answer: (d) the thickness, 0.86 cm

V = l × b × t, a product, keeps the fewest significant figures among its factors. The length and breadth have three, the thickness two, so the thickness limits the volume to two figures: 9.68876 cm³ is reported as 9.7 cm³. The mass does not enter the volume.

Part 3 · 2 marks

Find the density of the glass and report it correctly. Explain why the calculator's 2.59059 g cm⁻³ should not be written down.

Answer and marking scheme

The volume is 9.7 cm³ to two figures; keeping one extra digit in the intermediate volume (9.689 cm³), ρ = 25.1/9.689 = 2.59 g cm⁻³ by arithmetic, which is reported to two significant figures (set by the thickness) as 2.6 g cm⁻³. A result cannot be more precise than the measurements it is based on; 2.59059 suggests a precision the readings do not have and is misleading.

ρ = 2.6 g cm⁻³ (two figures) (1)
a result cannot be more precise than the data (1)

Meera's partner says the thickness should have been measured with a screw gauge. If the thickness is then 0.862 cm, how many significant figures can the volume and the density have, and why?

Answer and marking scheme

All four readings would then have three significant figures (5.24, 2.15, 0.862, 25.1), so the volume and the density could each be reported to three significant figures. In multiplication and division the least precise reading sets the figures; the metre-scale thickness, with two, was the limit.

three significant figures for both (1)
the least precise reading sets the figures in a product or quotient (1)

Chapter 2: Motion in a Straight Line →